Abstract.

This article addresses the control task for nonlinear system that can be presented as nonlinear differential system with linear structure and parameters depending on object state. Usage of quadratic cost function allows developing control with coefficients that include solution of Riccati equation in real time. The rather common way is to solve Riccati equation at rate of object functioning which requires high performance controller what is not appropriative in some applications. The method, represented in this article, is useful when system state space is compact and performance or weight of control hardware is critical. It is offered to calculate regulator coefficients in advance and to keep them in memory of the control device. Calculation of coefficients quantity and memory size depending on accuracy of calculations is provided. The mathematical simulation of aircraft controlled by such regulator was made for verification.

Keywords:

quaternion algebra, state dependent coefficients, Riccati equation, nonlinear dynamic systems.

PP. 64-70.

References

1. Pearson J.D. Approximation methods in optimal control // Journal of Electronics and Control, 1962
2. Mracek C.P., Cloutier J.R. Full envelope missile longitudinal autopilot design using the state-dependent Riccati equation method. // In Proc. of the AIAA Guidance, Navigation, and Control Conference. New Orleans, LA. 1997. pp. 1697-1705.
3. Afanasev V.N., Semion A.A. Regulyator s diskretno izmenyayuschimisya parametrami // Problemyi upravleniya, May 2014. pp. 14-20.
4. Alexander Bogdanov , Magnus Carlsson, Geoff Harvey, John Hunt, Dick Kieburtz, Rudolph van der Merwe, Eric Wan Statedependent Riccati equation control of a small unmanned helicopter // AIAA Guidance, Navigation, and Control Conference and Exhibit Austin, Texas 11-14 August 2003.
5. Semion A. A. Razrabotka avtopilota dlya kvadrokoptera // Kachestvo. Innovatsii. Obrazovanie. 2016. № 6. С. 53-67.
6. Branets V.N., Shmyiglevskiy I.P. Primenenie kvaternionov v zadachah orientatsii tverdogo tela. Moskva: Izdatelstvo "Nauka", 1973.
7. Yang, Yaguang Analytic LQR Design for Spacecraft Control System Based on Quaternion Model, Journal of aerospace engineering, 25, 3, JULY 2012., p. 448-453